Solving Trigonometric Equations Review

Linear Equations

100

All angles satisfying 3tanx=3 

What are 45 and 225 + 360n

200

All angles satisfying 2cosx-√3=0 

What are 30 and 330 + 360n

300

All angles satisfying 2sin(x) + 3 = sin(x) + 4

90 + 360n

400

The angle satisfying secxcosx+secx=0 on 0≤x<360

What is 180

500

The angles satisying 2sinx-1=3 on 0≤x<360

What is no solution?

Multiple Angles

100

The angles satisfying sin(2x)=-1 on 0≤x<360

What are 135 and 315?

200

The angle satisfying cos(x/2)=√3/2 on 0≤x<230

90

300

The angles satisfying cos(x-100)=-1/2 on 0≤x<360

220, 340

400

The angles satisfying cos(x/4)+1=0 on 0≤x≤720

720

500

The angles satisfying -sin(3x)=-√3 - 3sinx(3x) 

on 0≤x<360

20, 40, 140, 160, 260, 280

Unit Circle

100

The angles satisying sinx=-√2/2 on 0≤x<360

What are 225 and 315?

200

The angles satisftying cosx=-√3/2 on 0≤x<360

What are 150 and 210?

300

The angles satisfying cosx=-3/2 on 0≤x<360

What does not exist?

400

The angles satisfying tanx=-1 on 0≤x<360

What are 135 and 315?

500

The angles satisfying secx=2 on 0≤x<360

60, 300

Nonlinear Equations

100

The angles satisfying cos²x-1=0 on 0≤x<2π

What are 0, π?

200

The angles satisfying -3tan²x-4=-5 on 0≤x<2π

What are π/6, 5π/6, 7π/6, and 11π/6?

300

The angles satisfying 2cos³x+cos²x-cosx=0 on 0≤x<2π

What are π/3, π/2, π, 3π/2, and 5π/3?

400

The angles satisfying -2√3cscx-3csc²x=-6csc²x on 0≤x<2π

What are π/3 and 2π/3?

500

The angles satisfying sin²x=2+cos²x-3cosx on 0≤x<2π

What are 0, π/3, and 5π/3?

Miscellaneous

100

This is the hardest rock in the world

diamond

200

This is the smallest country in the world

Vatican City

300

In a website browser this is what "www" stands for

world wide web

400

The number of NFL football teams in the state of NY

3

500

As part of a Disney soundtrack, this song performed by the Rock just went 4x platinum

"You're Welcome"